The action of
\(\displaystyle \sigma \in W_F\)  on \(\displaystyle X(S\hat{})\)  induced from the action on \(\displaystyle S\hat{}\)  is such
that \(\displaystyle a_{\gamma }^{\sigma }=a_{\gamma \sigma }\)  for all
\(\displaystyle \gamma \in \text{\rm Emb}_F(K,\overline{F})\) , and it determines an
element \(\displaystyle w(\sigma )\in W(S\hat{})\) . Then
[1]} shows that the \(\displaystyle 2\) -cocycle
\(\displaystyle t\in Z^2(W_F,S\hat{})\)  defined by
\(t(\sigma ,\sigma ^{\prime })=n(w(\sigma \sigma ^{\prime }))^{-1}n(w(\sigma ))\cdot n(w(\sigma ^{\prime }))\quad (\sigma , \sigma ^{\prime }\in W_F)\) 
